The answer is grease Chris.
Final answer.
Presuming, that is, that you want to take the beggars apart and are confident that you can get the tension right when you reassemble them. So probably thin chain lube drizzled in and thoroughly wiped off afterwards. And wiped off again after a few miles. And again after a few more miles. The reality is that most modern brakes are so well sealed that they scarcely, if ever, need lubing.
Oh how I love coaster brakes.